Rigidity of saddle loops

Abstract

A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincar{é} rst-return map. We also prove that they are formally rigid when the Poincar{é} map is multivalued. Finally, we provide a list of all analytic classes of Liouville-integrable saddle loops.